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In 1985, while pursuing his doctorate in Clemson University, Autar Kaw revised a WPAFB Apple IIe based BASIC program for laminate analysis of composite materials. Since migration to PCs was not an easy task then (1988), he and a few hardworking independent study students wrote a completely new laminate analysis program called PROMAL. This tool was then used in teaching graduate level and senior elective course in Advanced Composite Materials course. Since 1988, PROMAL, which is now written in Visual Basic for Windows, has evolved into a product that is used in over 40 universities worldwide, and accompanies the Mechanics of Composite Materials textbook (1997).
Naturally, the success of this idea of developing computational tools was extended in 1990 to a course in Numerical Methods. At that time, we started developing simulations for Numerical Methods using Microsoft Quickbasic3.0, and then in Visual Basic for Windows.
In recent years with advances in mathematical packages and the web browsers/web development, and with funding from National Science Foundation, the idea was transformed to what it is now - extension to several mathematical packages and engineering majors. It is free of charge to anyone in the world.
To quote the OCW initiative at MIT, we are strong believers in "having open dissemination of educational materials, philosophy, and modes of thought, that will help lead to fundamental changes in the way colleges and universities utilize the Web as a vehicle for education." We are continually looking for self-sustaining avenues of dissemination, and we have been fortunate to find sponsors such as Maple and MathCAD to keep it free. |
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The core of undergraduate numerical methods consists mainly of eight topics/mathematical procedures, namely, 1) approximations, errors & modeling 2) nonlinear equations, 3) simultaneous linear equations including Eigenvalues/eigenvectors, 4) interpolation, 5) regression, 6) differentiation, 7) integration, 8) differential equations Under the NSF funding for the prototype, we developed modules for
1.
Nonlinear Equation
Under the second NSF grant approved in February 2004, we are developing four more modules. The following three modules have already been developed. 3. Integration 4. Ordinary Differential Equations
5.
Simultaneous Linear Equations The timeline for the other module is as follows. 6. Regression - August 2007
Under the third NSF grant approved in August 2007, we are developing five more modules. 7. Introduction to Scientific Computing 8. Differentiation
9. Fast Fourier
Transforms 11. Partial Differential Equations
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Q. Will all topics of numerical methods be included in the future and when? |
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To complete a typical Numerical Methods course, we have received funding for five more modules Introduction to Scientific Computing Differentiation
Fast Fourier
Transforms Partial Differential Equations
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There is no registration needed to use the course material. I want to keep it purely open access without any hassles or obstacles such as payment of use, registration, downloading, buying expensive software, etc. But drop me a note to tell me how you are using the resources. However, I am requiring faculty members who use any of the the course material to send me brief info and put link(s) to HNMI on their web site. |
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Faculty members can use the materials to enhance their classroom lecture by using the power point presentations and simulations. They can ask students to quickly assess their knowledge by taking the online assessment of multiple choice questions. They can ask students to pre-study the topics so that class time is used for discussion purposes. However, I am requiring faculty members who use any of the the course material to send me brief info and put link(s) to HNMI on their web site. This will help us to keep this site unrestricted and at the same time show where it is being used. |
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A student can use it to review background information on a topic, perform their own simulations, review course material, go for self-assessment of knowledge, learn how other engineering majors use numerical methods, have seven different examples to illustrate each method. |
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This courseware would only be possible with the web. We have taken a holistic approach where users can review the background information as well as see the higher level application of what they have learned. We have also taken a customized approach because had the contents been written in a a book form, one would have to write 28 versions of the book. But with this courseware, a student has 24/7 access and can work at his own pace with help from text book notes, simulations and assessment. |
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Q. What intellectual property policies govern the materials? |
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The materials given on the web site are mostly original and written by the faculty and students at the University of South Florida. Any other material is either in public domain, or permission has been given for its use and is acknowledged. If you have any questions about the ownership of the materials, please contact us. |
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The material on the web site or its derivatives can only be used for nonprofit purposes in educational institutions of any grade level. Providing direct links on user's website are critical in fair use of the materials. Any use of the material on the website should be acknowledged to the Holistic Numerical Methods Institute, University of South Florida, National Science Foundation and the original authors of the material. |
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The course was developed using Microsoft FrontPage and JavaScript for the web pages and assessment tools; Microsoft Office for the text notes and lecture presentations; Mathcad, Maple, Mathematica and Matlab for the simulations; Acrobat for making of the PDF files; Adobe Photoshop for editing images; Flash V for drawing sketches; Microsoft Publisher for advertisements. |
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Q. What are the system and technical requirements for the course materials? |
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Read all the system and technical requirements. |
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The Holistic Numerical Methods Institute is currently funded by National Science Foundation through their CCLI program. Support also comes from
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The long term goals of HNMI are to develop course materials for all the main topics taught in a course in Numerical Methods. This will depend on continued funding of the project. |
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Q. How does a faculty member contact a real person from HNMI? |
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Contact the Principal Investigator - Autar Kaw via telephone, e-mail, fax or mail. Any inquiry, especially from instructors of Numerical Methods, will be answered. We welcome your questions, comments, and suggestions. We would like to help you in incorporating the contents of the website in your course.
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Q. Why are the simulations, especially ones written in MATLAB not modular? |
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The simulations, especially those written in MATLAB, at first might appear not well written; they do not take advantage of modular programming. However, in our website modules, we wanted to keep all subroutines and functions within a single script file. This might not seem logical at first glance.
But, it is important to note the overall goal of the simulations is to provide the student only one file. The content is in one file for simplicity. Otherwise, there would be dozens of files that the student would have to manage and understand-- not just one.
Also we want to show a numerical method worked out step-by-step as if the student was working it out by hand. This is why many of the simulations show each iteration separately as opposed to in a loop.
We hope that you would ask your students to write procedures (subroutines, functions, etc) and use modular programming techniques as part of the learning process of Numerical Methods. |
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